Conformal Scaling Gauge Symmetry and Inflationary Universe

TL;DR

This paper proposes a model where conformal scaling gauge symmetry, broken by gauge fixing, leads to a scalar field-driven power-law inflation with a specific inflationary index, connecting gauge symmetry to early universe expansion.

Contribution

It introduces a gauge-invariant potential action based on conformal scaling symmetry and demonstrates how gauge fixing results in a power-law inflationary universe model.

Findings

Power-law inflation with scale factor a(t) ~ t^p.

Inflation index p is determined by gauge fixing parameter g_F.

For g_F=1, the model predicts p approximately 62.

Abstract

Considering the conformal scaling gauge symmetry as a fundamental symmetry of nature in the presence of gravity, a scalar field is required and used to describe the scale behavior of universe. In order for the scalar field to be a physical field, a gauge field is necessary to be introduced. A gauge invariant potential action is constructed by adopting the scalar field and a real Wilson-like line element of the gauge field. Of particular, the conformal scaling gauge symmetry can be broken down explicitly via fixing gauge to match the Einstein-Hilbert action of gravity. As a nontrivial background field solution of pure gauge has a minimal energy in gauge interactions, the evolution of universe is then dominated at earlier time by the potential energy of background field characterized by a scalar field. Since the background field of pure gauge leads to an exponential potential model of a scalar field, the universe is driven by a power-law inflation with the scale factor $a(t) \sim t^p$. The power-law index $p$ is determined by a basic gauge fixing parameter $g_F$ via $p = 16\pi g_F^2[1 + 3/(4\pi g_F^2) ]$. For the gauge fixing scale being the Planck mass, we are led to a predictive model with $g_F=1$ and $p\simeq 62$.